Question

A car is going round a circle of radius $R_{1}$ with constant speed. Another car is going round a circle of radius $R_{2}$ with constant speed. If both of them take same time to complete the circles, the ratio of their angular speeds and linear speeds will be

• A. $\sqrt{\frac{R_{1}}{R_{2}}}, \frac{R_{1}}{R_{2}}$
• B. $1,1$
• C. $1, \frac{R_{1}}{R_{2}}$
• D. $\frac{R_{1}}{R_{2}}, 1$

Answer 1

Answer: (C)

The angular speed is given by
$\omega=\frac{2 \pi}{T}$
$\omega \propto \frac{1}{T}$
$\Rightarrow \frac{\omega_{1}}{\omega_{2}}=\frac{T_{2}}{T_{1}}$
if $T_{1}=T_{2}$
$\Rightarrow \omega_{1}=\omega_{2}$
So, ratio $\Rightarrow 1: 1$
and linear speed $v=R \omega$
$V\propto R$
$\frac{V_{1}}{V_{2}}=\frac{R_{1}}{R_{2}}$